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This paper shows new general nonasymptotic achievability and converse bounds and performs their dispersion analysis for the lossy compression problem in which the compressor observes the source through a noisy channel. While this problem is asymptotically equivalent to a noiseless lossy source coding problem with a modified distortion function, nonasymptotically there is a difference in how fast their minimum achievable coding rates approach the rate-distortion function, providing yet anotherdoi:10.1109/tit.2016.2562008 fatcat:gvf4tpxkyrgczjzaxzxl4zxaca